How thermoelectric cooling works?

I`ve read that in thermoelectric cooling the current passes through a two different materials and because electrons start to slow down and radiate heat cooling is acheived.
But why not to use in this case a usual resistance instead of expensive metals?
For example we will place coper wire inside of refrigerator and resistance outside.When current
will pass through resistance it will dissipate heat.What would be difference from thermoelectricity?

You can get a small thermoelectric effect with metals (this is how thermocouples work) but since it depends on differences in work functions (metals) and/or Fermi levels (semiconductors), you can the largest effects with semiconductors, specifically ones related to Bi2Te3 which is common used in thermoelectric (Peltier) coolers.